Loudspeaker system having bass response range below system resonance

ABSTRACT

The subject patent application is concerned with improvements over prior art systems relative to the processing of the speaker back-wave by acoustic networks that include a part, and the use of the back-wave to produce supporting port radiation in a frequency band below the basic resonance frequency of the system. The structure includes essentially a pair of acoustic cavities, coupled by an aperture. The speaker is mounted in the first cavity. The second cavity may be subdivided and may include damping. A port aperture is included in one of the cavities. The improvements involve relationships between acoustic elements of inertance, capacitance and resistance that result in in-phase port radiation; and in relationships whereby smooth response is obtained while maintaining and improving the phase of port radiation relative to that of the speaker front-wave in the frequency region below system resonance. The present invention concerns only the bass and lower midrange frequencies, and is intended for operation with 6 db/octave amplifier equalization in the bass range.

United States Patent Hance 15] 3,690,405 [451 Sept. 12, 1972 SYSTEMRESONANCE [72] Inventor: Edwin A. I-Iance, 3920 Foothill Rd.,

Santa Barbara, Calif. 93105 [22] Filed: Feb. 24, 1971 [21] Appl. No.:118,482

Related US. Application Data [63] Continuation of Ser. No. 744,574, July12,

- 1968, abandoned, which is a continuation-inpart of Ser. No. 520,277,Jan. 12, I966, abandoned.

[52] US. Cl. ..181/31 B [51] Int. Cl ..Gl0k 13/00, H04r 1/28 [58] Fieldof Search ..181/31 B, 31 R [56] References Cited UNITED STATES PATENTS1,837,755 12/1931 Carlisle et al. ..l8l/3l B 2,766,839 10/1956 Baruch etal. ..l8l/3l B 3,239,028 3/1966 Murray ..l8l/31 B 3,371,742 3/1968Norton et al ..18l/31 B FOREIGN PATENTS 0R APPLICATIONS 1,142,754 4/1957France ..181/31 B Primary Examiner-Stephen J. Tomslry Attorney-Warren T.Jessup et a1.

[5 7] ABSTRACT The subject patent application is concerned withimprovements over prior art systems relative to the processing of thespeaker back-wave by acoustic networks that include a part, and the useof the backwave to produce supporting port radiation in a frequency bandbelow the basic resonance frequency of the system.

The structure includes essentially a pair of acoustic cavities, coupledby an aperture. The speaker is mounted in the first cavity. The secondcavity may be subdivided and may include damping. A port aperture isincluded in one of the cavities. The improvements involve relationshipsbetween acoustic elements of inertance, capacitance and resistance thatresult in inphase port radiation; and in relationships whereby smoothresponse is obtained while maintaining and improving the phase of portradiation relative to that of the speaker front-wave in the frequencyregion below system resonance.

The present invention concerns only the bass and lower midrangefrequencies, and is intended for operation with 6 db/octave amplifierequalization in the bass range.

22 Claims, 32 Drawing Figures I /42-- lagga 1 PATENTEDSEP I 2 I972 SHEET6 F 8 I I I I I 50 70 I00 140 200 am/W 4 /7( 4/I/C[ INVENTOR. BY W Q M II 50 70 I00 I 200 300 500 700 FQfOc/f/i/Cy LOUDSPEAKER SYSTEM HAVINGBASS RESPONSE RANGE BELOW SYSTEM RESONANCE This is a continuation ofapplication, Ser. No. 744,574, filed July I2, 1968, now abandoned, whichis a continuation-in-part of application, Ser. No. 520,277, filed Ian.12, 1966, now abandoned. BACKGROUND OF THE INVENTION The employment ofpiston-type direct radiator loudspeakers in the frequency region belowthat frequency for which the equivalent piston diameter is equal to aone-third wave length gives rise to severe problems. This inventionrelates to the employment of such loudspeakers in systems for thereproduction of sound in such frequency regions and the problemsassociated therewith.

One such problem arises from the requirement of separation of thespeaker back-wave from the frontwave as these two waves originate 180out of phase and will normally produce radiation cancellation at thelower frequencies. This problem is compounded when the physicalrequirements of the system are such that its dimensions must be smallrelative to the longest wavelength of sound to be reproduced.

Another such problem arises from the characteristics of acousticradiation resistance in this frequency region. This resistance variesinversely as the square of frequency. See Elements of AcousticalEngineering by H. F. Olson, page 82, FIG. 5.]. Thus, a speaker in aninfinite baffle must increase its cone excursion by a factor of four foreach time the frequency is reduced by a factor of one-half, if flatfrequency response is to be attained. This is the condition where thecone velocity is inversely proportional to frequency. See Elements ofAcoustical Engineering by H. F. Olson, page 128. The extension of bassrange in this type of system is, therefore, limited by the maximumpractical .excursion attainable.

The natural cone excursion characteristic, which corresponds to thatproduced when a speaker having constant reflected electrical impedanceis driven by a constant current, is one of constant velocity. Under thiscondition the cone excursion will be proportional to l/f (f==frequency)rather than the II} characteristic required for fiat response wheninfinitely baffled. Hence, a speaker operating in this mode will producea radiated sound .pressure characteristic that is proportional tofrequency; and if fiat response is to be achieved, the system must bedriven by an amplifier having a complementary l/f gain characteristic.This represents a compensation of 6 db/octave. See Elements ofAcoustical Engineering by H.F. Olson, pages 135 and 136.

. A further problem arises when the back-wave of the speaker is confinedby an enclosure that represents one or more acoustic elements havingvariable impedance characteristics relative to frequency. This problemis compoundedwhen the enclosure includes an aperture or apertures thatconduct acoustic volume current from the interior to the exterior. Underthe latter circumstance, the reflected electrical impedancecharacteristic of the system is in no way directly indicative of theactual radiated sound pressure of the system.

Answers to the problems that have been set forth are found in two typesof speaker systems that are in widespread current use. These are theacoustic suspension type and the bass-reflex type; however, each ofthese prevalent basic types has deficiencies of its own, leaving much tobe desired. The deficiencies of systems of the acoustic suspension typelie in their lower efficiency and in their large cone excursionrequirements. The deficiencies of systems of the bassreflex type lie intheir enclosure size requirements, being on the order of 2:1 greaterthan corresponding acoustic suspension types for a given bass range, andin their poor bass transient response characteristic. Although theoperational and performance characteristics of these two basic systemtypes are well known to persons skilled in this art, for the sake ofclarity, they will be briefly reviewed here.

The name acoustic suspension" takes its connotation from the concept ofsubstituting the acoustic capacitance of a confined volume of air forthe restoring force of the normally employed mechanical speaker conesuspension means. Ideally then, the cone resonance frequency would bethe same, with the restoring force supplied by a cushion of air trappedin a cavity totally enclosing the speaker back-wave. When this resonanceis optimumly damped, the system operates as a mass controlled pistonmounted in an infinite baffle and provides flat response for frequenciesabove cone resonance. Below the cone resonance frequency, the responsedrops off at a 12 db/octave rate. See Elements of Acoustical Engineeringby H. F. Olson, pages and 131.

In actual operation, however, the mechanical compliance of the conesuspension cannot be made infinite, and there is a tendency for the coneto mechanically distort due to the large one-sided acoustic reactanceinto which it faces. The cone and voice coil, therefore, are madeheavier than would normally be required. The efficiency, which islargely inversely proportional to the square of the piston mass, isthereby substantially reduced. See Elements of Acoustical Engineering byH.

F. Olson, page 112, formula 7.3, and page 1 13.

The name bass reflex takes its connotation from the employment of thespeaker back-wave in such a way as to reinforce the speaker front-wavein the bass frequency region. The utter simplicity of its form tends tobelie the subtlty of its operational and performance characteristics.This type of system can respond smoothly and efficiently down to thecone resonance frequency of the speaker employed. Below this frequencyboth the radiation response and the acoustic cone loading drop verysharply. For approximately one octave above this frequency, theback-wave reinforces the front wave and at higher frequencies the systemfunctions in essentially the same way as the acoustic suspension type.The speaker back-wave is enclosed by a cavity having a port or aperturecommunicating between the interior and the exterior of the enclosure.The acoustic capacitance of the cavity resonates with the acousticinertance of the port at the resonance frequency of the speaker cone,The mechanical reactances of the speaker cone and the acousticalreactances of the speaker enclosure are thereby coupled together into anetwork having the characteristics of a type of constant k electricalwave filter. An equivalent electrical circuit of the system, withexplanation and comments concerning the phase and impedancerelationships and their efi'ects, is given in Sidelights on LoudspeakerCabinet Design by D. E. L. Shorter, Wireless World, December 1950, page487.

The well-known reflected impedance characteristic of the speaker in thistype of system shows two sharp peaks, with a deep valley between themwhich centers on the speaker cone resonance frequency. Good results areachieved when the relationship between the speaker and enclosure volumeis such that the peaks are separated by a factor on the order of two toone in frequency. characteristically, the phase of the port radiationchanges abruptly at the cone resonance frequency and is nearly 180 outof phase with the speaker front-wave in the region of the lowerimpedance peak. See Radiotron Designers Handbook, fourth edition, page848, and Elements of Acoustical Engineering by H. F Olson, page 132,which also gives the equivalent electrical circuit. The result of thisis the sharp drop off in radiated sound pressure and in acoustic coneloading below the resonance frequency. This point in frequency may bemore accurately defined as the frequency of resonance of the enclosureacoustic capacitance with the acoustic inertance of the port, which isnormally the same as the cone resonance frequency. There is little, ifany, effective response in the region of the lower impedance peak, andthe response in the region between the valley center and the upperimpedance peak is sustained by port radiation produced from theresonance of the enclosure, resulting in poor bass transient response.

Various efforts have been made to combine the characteristics of thesetwo basic system types, but the results have been largely a matter oftrading off the disadvantages of one type against those of the othertype. Also various modifications have been taught in prior art. One suchmodification is taught by R. W. Carlisle, et al., in their U.S. Pat. No.1,837,755. The speaker cone and suspension are considered to resonatewith the speaker cone compartment at a definite frequency. This is inkeeping with the concept of the acoustic suspension type of system. Theobject of the invention is expressed as that of critically damping thisaforementioned resonance by acoustical means. In its preferredembodiment, an additional cavity is coupled to the speaker compartmentby means of an aperture and substantial damping is employed in relationto the coupling aperture. Also, an aperture or port is showncommunicating between the interior of the added cavity and the exteriorof the system and having substantial damping associated with it. Thepreferred damping technique is that of employing flow resistance in theregion of the apertures. Inasmuch as no mention is made of either usefulport radiation, or port radiation phase, it is evident that the intentis one of substantially destroying the speaker back-wave energy beforesuch energy has the opportunity of producing exterior radiation. Thisbeing the case, the system operates in essentially the same way as theacoustic suspension type with optimum damping achieved acousticallyrather than electrically.

Another modification, shown for example in Baruch Lang, U.S. Pat. No.2,766,839, is taught wherein a bass reflex system is deliberatelyreduced below its optimum enclosure volume, and modifications are madeto reduce the resulting deficiencies. The system is designed with theintention of being operated at the intersection of three mutuallyperpendicular surfaces, which would normally be the comer of a room.This placement provides improved radiation resistance at the bassfrequencies. Response curves given are made from measurements takenunder these conditions.

The undersize enclosure volume results in a strong peak in response inthe region of the upper impedance peak which is difficult to suppress.Suppression of this peak is accomplished by dividing off a portion ofthe enclosure cavity with a partition having an array of holes in it,which constitute an aperture, and flow-resistance damping is employed inconjunction with the holes. The acoustic inertance of the aperture issuch as to resonate with the divided-off portion of the cavity at afrequency corresponding to the upper impedance peak. The radiationresponse curves given show little advantage due to the modificationother than suppression of the response peak referred to. The basicsystem functioning is the same as that of the ordinary bass reflex type.

A still further modification is taught in Leon, French Pat. No.1.142.754, wherein the normal acoustical configuration of the bassreflex type of system is altered by partitioning the enclosure into twocavities, the second cavity being coupled to the first by one or moreopenings or slits in the partition, This alteration is also shown inapplication to a speaker mounted in an unvented enclosure. Reference ismade to the curve of reflected electrical impedance as an expression ofthe acoustic pressure on the speaker cone relative to frequency, and theregulation of this curve in the vicinity of a horizontal line isreferred to as being the criterion of improvement of speaker systemperformance.

The typical two-peak and valley reflected electrical impedance curve ofthe bass reflex type of system is presented as one in which improvementsare made in accordance with the teaching. The alleged improvementresulting from the application of the teaching is shown by an electricalimpedance curve wherein the two impedance peaks are merged into one newbroad impedance peak centered on the frequency that was formerly that ofthe valley. No mention is made to either the amount or phase of portradiation, or to the required llf cone excursion characteristic, whereno port radiation exists. While Leon alludes to the incorporation ofadditional partitions to create new cavities, he gives no criteriawhatever for their design, nor any hint of what different results wouldfollow. it is significant that Leon shows no measurements of actualradiated sound output relative to frequency. it is evident that he madeno such measurements, for had he done so, he would have found that thecurve of actual radiated sound output bears little correlation to theimpedance curve, shown for example in FIG. 4 of the Leon patent. Thus,Leons FIG. 4, which neatly optimizes the electrical impedance curve, isassociated with a corresponding curve of acoustic output which drops offsharply at frequencies below his original upper peak.

SUMMARY OF THE INVENTION This invention relates to the application ofcertain modifications and relationships to the basic acoustic systemconfiguration of two cavities, a speaker, a port aperture, and couplingaperture means between the two cavities. This configuration bears somesimularity to that shown in FIG. 2 of the Leon patent, French Pat. No.l.l42.754. When my modifications and relationships are applied to thisacoustic configuration, different basic modes of operation are achievedwhich have important advantages over systems and techniques taught inthe prior art..

These modifications and relationships result in a type of system thatfunctions in the manner of constant impedance over the first two octavesof frequency range, and, therefore, it is intended for operation withamplifier frequency compensation of 6 db/octave over this portion of itsrange. Unlike other basic system types, this type of system producessubstantial and effective radiated sound pressure in the octave belowsystem resonance, and the speaker front-wave is supported by strongin-phase port radiation in this frequency region. The port radiation iseffective in increasing both the frequency range and the power handlingcapability of the system. This is achieved without detriment to thefrequency response characteristic above system resonance.

The system efficiency has a rising characteristic over the first twooctaves that complements the amplifier frequency compensation. Themid-range efficiency tends to be correspondingly greater than that ofother systems having the same frequency range and size of speaker andenclosure. The net result is one of substantially greater effectiveoverall efficiency.

With the proper amplifier frequency compensation, this type of systemwill produce a substantially flat radiated sound pressure characteristicover the frequency range of concern. The system may be convenientlycharacterized by a unique relationship between speaker cone area,enclosure internal volume, and system resonance frequency. By the meansof analysis and experimental investigations, I have determined what thisrelationship is and have incorporated it into a generalized formula fromwhich the necessary basic design parameters can be determined.

In the preferred form of the invention, the loudspeaker is incorporatedwith an enclosure having an overall volume similar to that required foroptimum performance in the normal bass reflex type of system. Theenclosure is divided into two main compartments or cavities comprisingacoustic capacitances which are coupled together by an aperture orducting means comprising an acoustic inertance. The speaker compartmentcavity is also coupled to the exterior atmosphere by an aperture orporting means comprising an acoustic inertance. These acousticinertances are maintained as low in loss at the frequencies of primaryconcern as is reasonably feasible. The values of the acoustic inertanceelements are so adjusted that together with the acoustic capacitancesand the reactive mechanical elements of the speaker cone, they produce ashort circuit terminated acoustic band-pass filter. The system thus fardescribed corresponds to an electrical constant k" band-pass filter.

The short-circuit terminated end of the acoustic filter is the secondcavity. The reflected electrical impedance curve of this system is nowcharacterized by three impedance peaks, one in the region of l/2F,., onein the region of F,, and one in the region of 2 F,, where F, representsthe speaker cone resonance frequency. Thus, the three impedance maximamay be said to delineate a first and a second frequency band, each onthe order of one octave in width, with the second sequentially followingthe first in frequency. Also, the frequency region between the uppermostimpedance peak and the frequency above which the radiation resistancebecomes constant may be considered as a third frequency band. Veryimportant phenomena are produced by the reflected sound energy from thesecond cavity in the first and second frequency bands, resulting in portradiation characteristics that are inverted from those of the normalbass reflex system. This radiation maximizes in the lower frequencyportion of the first band and in the upper region of the second band.The phase of this radiation is substantially the same as that of thespeaker front-wave in the mid region of the first band, and strongsupporting radiation occurs. In the second hand, the phase of portradiation is such as to interfere with the speaker front-wave and this,combined with a high acoustic back-wave impedance, produces a deepvalley in radiated sound output in the mid-band region. In the thirdband the system functions essentially the same as the acousticsuspension type.

In this invention the reflected energy that produces the deep valley ofresponse in the second band is selectively absorbed in a way that doesnot appreciably alter the system operation in the first and third bands.This is accomplished by altering the second cavity in such a way as toproduce an acoustic band-pass filter subsystem whose pass-bandencompasses the region between the center and upper impedance peaks, andwhose lower cut-off frequency coincides with the center reflectedimpedance peak, producing an acoustic impedance minimum at this point inthe shortcircuit terminated condition so that the reactancecharacteristic and acoustic functioning of the system remain essentiallyundisturbed. The filter sub-system is then provided with an acousticresistance termination, thus absorbing the energy as stated. Theout-of-band rejection of the sub-system filter increases rapidly beyondits theoretical cut-off frequencies, hence, the effect on the first andthird bands is minimal.

The operational characteristics of the system are different in each ofthe three frequency bands. The basic acoustic band-pass network has acharacteristic acoustic impedancelthe electrical counterpart is equal toVIJC) which reflected in the electrical impedance of the speaker. Thedynamic source resistance of the driving amplifier is coupled to theacoustical network through the electroacoustical transductance of thespeaker. In keeping with network theory, it is desirable that thissource resistance be matched to the network characteristic impedance.Under this condition, in the first band the system operates in themanner of a bandpass filter that is terminated in a short circuit, butis driven by a generator of matching impedance. In the second band theoperation is similar, but the filter is terminated in a resistancerepresenting a matched load. In the third band, the system is unmatchedas there is no characteristic impedance as such in this region and itsoperation is substantially that of a mass-controlled piston in aninfinite baffle or acoustic suspension system.

Thus, in the first and second bands the operation is essentially that ofa matched system and, therefore, has a radiated sound pressure responsecharacteristic that rises at a rate of 6 db/octave with frequencythrough the two-octave range. Flat response is attained by incorporatinga reverse frequency slope in the driving amplifier which can be donewith a simple resistancecapacitance network. The system operated in thisway provides relatively uniform frequency response down to one-half F Inthe lower portion of the first band the acoustic power output for agiven cone excursion is on the order of four times that of an equivalentacoustic suspension system so that only about one-half the coneexcursion is required.

Also, the efficiency in the region of one-half F, is essentially thesame, and rises at the 6 db/octave rate, becoming on the order of 12 dbgreater in the region of the third band. In comparison with acorresponding bass reflex system, the third band efficiency is the same,but the efficiency drops ofi in the second and first bands. Anadditional octave of useful response is gained for a given enclosuresize, and the bass transient ringing is substantially eliminated througha more gradual roll-ofi' and phase rotation.

To gain the same response range from a corresponding bass reflex systemwould require an increase in cone assembly mass of four times so as toproduce an octave drop of the cone resonance frequency. The effect onmid range efficiency would be a loss of 12 db.

This invention also includes an additional modification that furtherimproves the speaker acoustic loading in the region of one-half F,,thereby further reducing the required cone excursion. This improvementis effected by deflecting the air particle velocity of the acoustic portcurrent in the direction of the speaker cone. In this frequency regionthe port volume current phase in reference to that of the cone motion issuch as to augment the radiation impedance. In this way the effectiveradiation resistance is increased at the lower frequencies.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. IA is a diagram of the acousticsuspension" type of system t W 7 FIGJB (dotted curve) is reflectedelectrical impedance characteristic of an acoustic suspension type ofsystem. (Solid curve) illustrates the radiated sound pressurecharacteristic of an acoustic suspension type of system. FIG. 1C (dottedcurve) illustrates the reflected electrical impedance characteristic ofan infinite baffle? type of system. (Solid curve) illustrates theradiated sound pressure characteristic of same.

FIG. 2A is a diagram of a bass reflex type of system.

LII

FIG. 3D (dash curve) illustrates the uncompensated radiated soundpressure characteristic of the system of FIG. 3C. (Solid curve)illustrates the compensated radiated sound pressure characteristic ofthe system of FIG. 3C.

FIG. 4A is a diagram of a basic two-cavity and port system (undamped).

FIG. 4B illustrates the compensated radiated sound pressurecharacteristic of the system of FIG. 4A.

FIG. 4C is the equivalent electrical circuit of the second cavity.

FIG. 5A is a diagram of the modified second cavity without terminationand referencing acoustic elements.

FIG. 5B is the equivalent electrical circuit of the lower half of thesystem shown in FIG. 5A, including the coupling aperture from thespeaker compartment to the lower half of the system.

FIG. SD (solid curve) illustrates the reflected electrical impedancecharacteristic of the system of FIG. 4A with se con i cavity modified,but unterminated (Dotted curve) is deviation of impedanae characteristicfrom unmodified system in FIG. 4A.

FIG. 6A is a diagram of modified system with flowresistance termination.

FIG. 6B is the reflected electrical impedance characteristic of systemin FIG. 6A.

FIG. 6C (solid curve) illustrates the radiated sound pressurecharacteristic of the system in FIG. 6A. The dotted curve is the same asthe solid curve in F IG.3D.

FIG. 6D is a diagram of the system of FIG. 6A. except with soundabsorbing material within the second sub-cavity for the termination.

FIG. 7 (dotted curve) illustrates the radiated sound pressurecharacteristic of the system in accordance with the invention and havingthe correct internal volume in accordance with formula. The solid curveis the characteristic with one-half correct volume.

FIG. 8A is a diagram of a modified system with unequal cavity volume.

FIG. 8B (dotted curve) illustrates the reflected electrical impedancecharacteristic of an unequal cavity, unmodified system. The solid curveillustrates the reflected electrical impedance characteristic of thesystem in FIG. 8A. The dash curve illustrates the radiated soundpressure characteristic of the system of FIG. 8A.

FIG. 9A is a diagram of the two-cavity system with port in secondcavity. referencing acoustic elements.

FIG. 9B (dotted curve) illustrates the reflected electrical impedancecharacteristic of the system in FIG. 9A. The solid curve illustrates theimpedance for the system in FIG. 9A, after modification.

FIG. 9C (dotted curve) illustrates the radiated sound pressurecharacteristic for the system in FIG. 9A. The solid curve illustratesthe radiated sound pressure for the system in F I G. 9A withmodifications.

FIG. 9D is a diagram of a modified system with port in second cavity.

FIG. 10A is a plan section taken on line l0A-IOA in FIG. 10B of thepreferred system with all improvements.

FIG. 10B is a sectional elevation taken on line 108- IOB in FIG. 10C ofthe preferred system with all improvements.

FIG. C is a cross section in elevation taken on line 10C-10C in FIG. 10Aof the preferred system with all improvements.

FIG. 10D is a front elevation of the preferred system with allimprovements.

9 (s l d, r e) i r s t efii ate sound pressure of the preferred system.The dotted curve illustrates the reflected impedance of the preferredsystem.

FIG. 11 (solid curve) illustrates the response of the system with 5-inchspeaker, following formula. The dash curve illustrates the amplifierequalization curve for the above. The dotted curve illustrates therelative response of an 8-inch acoustic suspension system,forcomparison.

DESCRIPTION OF THE PREFERRED EMBODIMENT In the process of pursuing andevaluating the invention various other systems were investigated andtheir reflected electrical impedance characteristics were measured, aswell as their radiated sound output response characteristics. Some ofthese measurements are pertinent to the presentation and understandingof the invention. These measurements have been made in the same mannerand with the same equipment in each case. The reflected electricalimpedance measurements have been made with a resistance bridge bybalancing out the DC. voice-coil resistance component of impedance andcalibrating the balance error signal. These measurements, therefore,include the blocked voicecoil winding inductance which is a negligiblefactor at the bass frequencies. Relative sound output phase measurementshave been made with a microphone that is sensitive to the pressureingredient of the wave only, so that near field sound velocity effectswere eliminated which otherwise could give erroneous results.

Radiated sound output measurements were made with the microphone andspeaker placed adjustment to the earths surface as a ground plane, sothat the wavefront emanated perpendicular to the ground plane, thuseliminating reflections in the frequency region of concern. Possibleerror from waveform distortion or stray signal pickup was eliminated bymonitoring the microphone output with a Lissajou oscilliscope pattern.Also, these measurements were made well away from major sound reflectingobstacles. See E. W. Kellogg, Journal Acoustical Society of America,Vol. 2, No. 2 Oct. 1930, pages 175, 185-187.

With the exception of an acoustic suspension type of system, themeasurements were made of systems employing the same loudspeaker in anenclosure having the same overall internal volume. With this exception,the speaker employed throughout was an Altec Model 4008, which is an8-inch cone-type speaker of professional quality and good efficiency.The cone functions essentially as a piston on the frequency rangeinvolved. The cone resonance fr e quen cy is 'IA I -I when rib used onrhdiiifit baflle. The same enclosure was used, being altered in eachinstance to produce the type of system under investigation, and theeffective internal volume was held constant at 1.2 cubic feet.

I have used the same speaker and enclosure conditions for evaluation ofsome of the embodiments of this invention, thereby enabling direct andmeaningful comparisons to be made. In each case presented, a

limited amount of sound-absorbing material was employed on the walls ofthat part of the enclosure that comprised the speaker compartment. Thiswas necessary to prevent internal reflections from causing peaks orvalley in the 250- to 1,000-cycle region. The amount employed wasinsufficient to produce any noticeable effect on the low-frequencyoperation with the exception of a bass-reflex system wherein additionaldamping was required to produce optimum smoothness of lowfrequencyresponse. Where the enclosure consisted of more than one compartment orcavity, the sound absorption was limited to the speaker compartmentonly.

The simplest form of loudspeaker and enclosure system is that of theacoustic suspension" type. My observation is that good quality acousticsuspension systems rely heavily on electrical damping to produce thedesired cone excursion vs. frequency characteristic for flat radiatedsound output. I have measured the reflected electrical impedance and theradiated sound pressure vs. frequency of a high quality, well-known andaccepted system of this type, employing an 8-inch speaker. An acousticdiagram of the system appears in FIG. 1A. FIG. 1B shows the electricalreflected impedance and the radiated sound pressure output in relativelinear units. Sound power output is proportional to the square of soundpressure. The dotted curve represents the reflected impedance and thesolid curve represents the sound pressure output. It is obvious thatthere is little resemblance between the two curves. The resonancefrequency of the system is indicated by the peak of the reflectedimpedance curve. Below this frequency the response falls off at a rateof 12 db/octave. This particular system is slightly underdamped, givingrise to the peak in response just above the resonance frequency. SeeRadiotron Designers Handbook, 4th Ed., page 845, FIG. 20.12. The dampingfactor of the amplifier employed was very high. The internal volume ofthe enclosure is approximately 10.65 cubic feet.

Although it is in reverse order as to the historical sequence ofdevelopment, the next logical step in complication of a loudspeaker andenclosure system is that of adding stiffness to the cone suspension,thus creating the infinite baffle type of system. This stiffness adds tothe stiffness of the air trapped in the cavity behind the speaker andthus increases the resonance frequency of the system, resulting in areduction of bass response range. However, an optimum amount ofstiffness can aid the mid and and upper mid-range efficiency andsmoothness of response. I have measured the reflected electricalimpedance and the radiated sound pressure characteristic of such asystem using the speaker and enclosure which I have described.

The basic structural form was essentially the same as that shown in FIG.1A. The dotted curve in FIG. 1C shows the reflected electricalimpedance. The solid curve in the same figure shows the radiated soundpressure. The same driving amplifier was used as was for the acousticsuspension system measurements.

Again, there is little resemblance between the radiated sound pressureoutput and the reflected electrical impedance curves. The cone resonancefrequency of the speaker was increased from 74 to cycles by theenclosure. Although the reflected impedance at 95 cycles is on the orderof 20 times that which it is at 300 cycles, the actual response is downat least 6 db. This is due to excessive electrical damping. Again, seeRadiotron Designers Handbook, 4th Ed. page 845, FIG. 20.12.

The apparent loss of bass is only relative. Actually, it is not so mucha loss of bass as it is an increase in midrange efficiency. This can becountered by the use of a lower amplifier damping factor or bycompensation of the amplifier frequency response. The results clearlyindicate that, with the electrical efficiency available in modernspeakers, adequate damping of the resonance of the speaker cone and itscompartment is readily achieved electrically and that special techniquesfor additional acoustic damping as taught by Carlisle, U.S. Pat. No.1,837,755, are not necessary where the enclosure is essentially aninfinite baffle.

I have altered this infinite baffle system to produce operation as abass reflex type by providing an aperture opening between the interiorand exterior of the enclosure. The area of the aperture was adjusted toproduce the correct value of acoustic inertance to resonate with theacoustic capacitance of the enclosure cavity at the speaker coneresonance frequency. A diagram of the acoustic configuration is shown inFIG. 2A. The dotted curve in FIG. 2B shows the reflected electricalimpedance, and the solid curve in the same figure shows the radiatedsound pressure.

Here there is even less resemblance between the reflected electricalimpedance curve and the actual radiated sound output curve. The valleyminimum point between the two reflected impedance peaks represents theresonance frequency of the system. Although the impedance rises andreaches a strong peak below this frequency, the sound output breakssharply at this point and continues to drop. My measurements indicatethat the phase of port radiation relative to that of the speakerfront-wave reverses abruptly at this frequency, below which it islargely 180 out-ofphase with the speaker front-wave. Hence, not onlydoes the response drop abruptly, but so also does the acoustic coneloading, resulting in a correspondingly sharp drop in power handlingcapability. The increased bass response of this system over that of theinfinite baffle system shown by the solid curve in FIG. 1C is the resultof supporting port radiation augmented by strong acoustic resonance inthe frequency region encompassing system resonance and the upperimpedance peak.

Also, in the course of evaluating the invention, I have modified thisspeaker and enclosure bass reflex system in accordance with the teachingof Leon, French Pat. No. 1.142.754, for the purpose of damping theacoustic resonances that produce the reflected impedance peaks andevaluating the resulting radiated sound output vs. frequencycharacteristic. I partitioned the enclosure into two cavities, as shownin FIG. 3A, the speaker and port being in the first, and the secondbeing coupled to the first by a plurality of )-inch holes through thepartition wall. The number of coupling holes was adjusted to produceresonance with the second cavity acoustic capacitance at the speakercone resonance frequency. The area of the port aperture was likewiseadjusted to resonate with the acoustic capacitance of the first cavityat the speaker cone resonance frequency. The resulting reflectedelectrical impedance is illustrated by the solid curve 121 in FIG.

3B. As shown, it is characterized by three major peaks, a characteristicthat had not been noted by Leon in his patent. Also, there is littleevidence of acoustic dampmg.

Leon refers to the use of openings or fentes" which can be interpretedas slits." Whatever Leon used, it appears to have produced substantiallymore acoustic damping (resistance) that the holes which I employed. Forthis reason, I added flow-resistance damping in a manner similar to thattaught by R. W. Carlisle in U.S. Pat. No. 1,837,755, and by J. J.Baruch, U.S. Pat. No. 2,766,839.

Using the same configuration, I clamped layers of cloth between thedividing panel and an additional member containing a group ofcorresponding and aligned holes, as illustrated in the diagram FIG. 3C.After much experimenting with different materials I was able to producethe reflected electrical impedance characteristic shown by the dottedcurve 123 in FIG. 3B, which represents the most uniform characteristicthat I was able to attain. I then measured the radiated sound-pressureoutput which is shown by the dash curve in FIG. 3D. It is obvious that,although the reflected electrical impedance characteristic of thissystem is far more uniform that that of the simple bass reflex system,its performance is very inferior. Also, it is evident that this was notforeseen by Leon, as he taught in his patent that the performance ofsuch systems could be evaluated from the curve of impedance," referringto reflected electrical impedance, and that the criterion of improvedperformance is the regulation of this curve more in the vicinity of astraight and horizontal line.

It can be seen from the dotted reflected electrical impedance curve 123in FIG. 33 that the impedance is relatively uniform over a nearly 4:1frequency range commencing in the region of one-half the cone resonancefrequency. Therefore, the cone excursion vs. frequency can be expectedto largely follow a l/f (f=fr equency) characteristic. As previouslynoted, such a characteristic, when associated with an infinite planebaffle or total enclosure, results in a radiated sound pressure responsethat is proportional to frequency, and the required 1/ f excursioncharacteristic for flat response may be realized through the employmentof frequency response compensation in the associated amplifier system.

The required frequency slope of 6 db/octave over the necessary frequencyrange is obtainable by the employment of a simple R/C network at theamplifier input terminal. When this equalization is employed with thesystem of FIG. 3C, the resulting sound pressure radiation response is asshown in the solid curve in FIG. 3D. There is still severe loss ofresponse in the region of speaker cone resonance and below, and the basspower handling capability is correspondingly poor.

I have found that this drop-off of response is directly attributable tothe amplitude and phase differential of port radiation, relative to thatof the speaker frontwave, and that the phase differential is primarilythe result of dissipation of the speaker back-wave energy in theintercavity coupling means (the flow resistance associated with theholes between the two cavities in FIG. 3C.)

It was the investigation of this basic two-cavity and port type ofsystem acoustic configuration that lead to my invention. 1 found thatwhen a relatively low-loss coupling aperture means was employed betweenthe two cavities, the system took on new characteristics that werebasically different from the other systems and from the normal bassreflex system. To minimize losses, I used a single aperture to couplethe cavities.

A diagram of the acoustic arrangement appears in FIG. 4A. The speaker101 was mounted to and as a portion of the exterior wall of the firstcavity 102 (Ca-1). The inertance of the port aperture 103 (Ia-1) wasadjusted so as to resonate with Ca-l at the resonance frequency of thespeaker cone. The intercavity coupling aperture 104 (Ia-2) was likewisead- .justed so as to resonate with the second cavity 105 (Ca- 2) at thespeaker cone resonance frequency.

For convenience of reference, I will hereafter refer to the speaker-coneresonance frequency as F,, the frequency of resonance of the portaperture with the first cavity as Fr-Cl, and the frequency of resonanceof the coupling aperture with the second cavity as F The reflectedelectrical impedance curve of this system is characterized by threemajor impedance peaks instead of the two associated with the normal bassreflex system. The impedance curve of the speaker in the enclosure asdescribed is essentially identical to the solid curve in FIG. 38.However, the prime difference between this system and the bass reflexsystem lies in the phase vs. frequency characteristic of port radiationrelative to the speaker cone front-wave. I

found that the phase of the port radiation is substantially the same asthat of the speaker front-wave in the region of the lower impedancevalley and that it gradually rotates toward a 180 differential as thefrequency was lowered, passing through 90 in the region of the lowerimpedance peak. Thus, in the frequency region below F,, the portaperture radiation is substantially in-phase with the speaker conefrontwave and provides substantial supporting radiation down toapproximately one-half F In the region above F,, the port radiationphase is such as to be destructive, and this, combined with a region ofhigh acoustic backwave impedance, results in a severe valley in theradiated sound pressure response, located between the center and theupper reflected electrical impedance peaks. Using the 6 db/octaveamplifier frequency response compensation as described, the radiatedsound pressure characteristic of this system is as shown by the curve inFIG. 4B.

This basic two-cavity undamped system showed several importantadvantages over other systems. These included effective radiation withport radiation support in the octave frequency band below F,, as well ascomparatively small size. However, these advantages were unimpressiveunless the valley in the radiated response could be eliminated, andunless a comparatively smooth transition in responsebetween thecompensated low frequency region and the uncompensated upper frequencyregion could be effected. I have devised certain modifications andrelationships that overcome these problems and provide some furtherimprovementin low frequency range.

I have found that the source of both the extended bass frequency rangebelow F, and the valley in dissipate the energy in the response valleyregion without seriously interfering with the lower frequency response.This I have accomplished in a unique way.

I have devised a technique for modifying the second cavity in such a waythat its reactance characteristic is essentially unaltered in respect tofrequencies below F,, while above F, the cavity behaves as a band-passfilter and termination sub-system that effectively dissipates the energyin the response valley region without substantially affecting the energyin the lower frequency region.

The functioning of the unmodified second cavity is analogous to that ofthe series resonant electrical circuit shown in FIG. 4C. In both cases,the input impedance approaches zero at the frequency of resonance.

The theory of operation of the band-pass filter is essentially the sameas that of the equivalent electrical wave filter. A diagram of theacoustic configuration with zero acoustic terminating resistance isshown in FIG. 5A. A circuit diagram of the equivalent electrical filterappears in FIG. 5B. This circuit when short-circuit terminated, producesresonance at four frequencies, two of which can be referred to ascut-off frequencies. At the filter input terminal, the first or lower ofthese two frequencies appears as a point of near zero impedance, and thethird appears as a point of near infinite impedance. Their location canbe predetermined by proper calculation of circuit element values. Partof my technique is the substitution of the lower cut-off frequency forthe unmodified second cavity resonance frequency F r-C2.

The acoustic and electrical elements shown in FIGS. 4A, 4C, 5A and 5Bare analogous as follows:

Acoustic capacitance, which is produced by cavity volume, is analogousto electrical capacitance.

Acoustic inertance, which is produced by the reactance of apertureopenings and any ducting associated with them, is analogous toelectrical inductance.

Acoustic resistance, which is produced by sound-absorbing material orflow-resistance, is analogous to electrical resistance.

In general, and for the purpose of this presentation, the followingrelationships may be considered to be essentially correct.

Where the physical dimensions are small relative to the wavelengthsinvolved,

Acoustic capacitance is proportional to cavity volume;

Acoustic inertance is inversely proportional to aperture area where thepath-length through the opening is held constant, and where the apertureis of a slot-type and the area is varied by changing the slot length.

Referring to FIGS. 4A and 4C, the specific analogue counterparts are asfollows:

Ia-2 intercavity coupling aperture 104, corresponds to L10.

Ca-2 second cavity 105, corresponds to C10.

Referring to FIGS. 5A and 5B, the specific analogue counterparts are asfollows:

Ia-2a coupling aperture 111 from the speaker compartment cavity 112 tothe first sub-cavity 1 13, corresponds to L1.

Ia-2b coupling aperture 1 14 between the first subcavity 113 and thesecond sub-cavity 116, corresponds to L2.

Ca-2a first sub-cavity 1 13, corresponds to C1.

Ca-2b second sub-cavity 1 16, corresponds to C2.

As shown in FIG. A, the second cavity 117 is divided into two coupledsub-cavities 113 and 116, the sum of their volumes being equal to thatof the original second cavity 105 in FIG. 4A.

The band-pass filter consists of a constant k type of transmission arm,L1 and Cl, followed by a series resonant terminating arm, consisting ofL2, C2 and RL. In the acoustic case the transmission arm is representedby 111 (Ia-2a) and 113 (Ca2a) ,and the series resonant terminating armis represented by 1 14 (Ia-2b) and 116 (Ca-2b). Since no damping or fiowresistance is shown in conjunction with Ia-2b or Ca-2b in FIG. 5A, RL inthe equivalent electrical circuit 58 would be equal to zero.

Let it be assumed that the system of FIG. 4A is constructed with optimumparameters to produce the response of FIG. 48. An arbitrary referencevalue of one will be assigned to Ia-2 and an arbitrary value of 1 willbe assigned to Ca-2 in such optimum system. If the system is nowmodified to the system of 5A, by dividing Ca2 into Ca-2a and Ca-Zbcavities of equal volume, then Ca-2a plus Ca-2b must equal Ca-2. Thus,each will have a value of 0.5.

I have found that the apertures 111 and 114 should each have an area onthe order of 1.25 times the area of aperture 104 (FIG. 4A) for optimumperformance of the modified system shown in FIG. 5A, where a slot typeof aperture is used and the area increased by lengthening the slot. Bymathematical analysis of an optimum electrical system constituted perthe a analogy of 58, I have found that L1 and L2 should each be 0.765times L in FIG. 4C. Since inertance I is essentially proportional to thereciprocal of aperture area in this case, it follows that thecorresponding calculated optimum area for Ia-2a (111) and Ia-2b (114)would be l/0.765 or 1.3 l, very close to the actual area noted. Exactcorrelation is not possible because of the partially distributed natureof Ca-Z, Ca-2a, and Ca-2b. Also, the relative distributed effect isaltered by the division of Ca-2.

In reference to the electrical analogue system in FIG. 58, when thevalue of 0.765 is assigned to L1 and L2, and the value of 0.5 isassigned to C1 and C2, which corresponds to the acoustic case, thefollowing unique relationships exist.

I. The lower cut-off frequency of the filter is the same as that of theresonance of L10 with C10 in FIG. 4C, which corresponds to theunmodified second cavity.

2. In the octave below the lower cut-off frequency, the input impedanceof the filter when RL=0 is essentially identical to that of the seriesresonant circuit of L10 and C10 in FIG. 4C.

3. The resonance frequency of L1 with C1, and L2 with C2 is at 1.62times the resonance frequency of L10 with C10 (F,

4. The frequency of resonance of L2 with C1 and C2, which may bereferred to as the upper cut-off frequency of the filter, is at 2.29times the frequency of resonance of L10 with C10 (F These relationshipshold substantially the same for the acoustical case. As a result, themodified second cavity 117 in FIG. 5A functions essentially the sameacoustically as the unmodified second cavity in FIG. 4A.

The solid curve of FIG. 3B represents the electrical impedance of thesystem of FIG. 3A. The systems of 3A and 4A are the same, except that 3Aemployed 16 onehalf-inch holes between the cavities, whereas 4A employeda pair of crossed slots, each arm being approxi mately 3 by Binches. Theimpedance curves were very similar, as may be seen by comparing thesolid curve of FIG. 38, with the dotted curve of FIG. 5D, the latterrepresents the impedance of the system of FIG. 4A.

Referring again to the solid curve in FIG. 38, it can be seen that thevalley 122 between the middle and upper reflected impedance peaks is atessentially l.6 times the frequency of the middle peak 121 (F and thatthe upper impedance peak 123 is at slightly more than twice thisfrequency. Hence, the frequency of resonance of the filter armscomprised by the modified second cavity (117 in FIG. 5A) substantiallycoincides the valley fr equgncy, while the lower cut-off frequencycoincides with the middle impedance peak 121, and the upper cut-offfrequency falls somewhat above the upper impedance peak.

A simple way to show that the function of the bandpass filtermodification of the second cavity is essentially the same as that of theunmodified second cavity before the incorporation of terminatingresistance is to calculate the relative reactance produced by each at asignificant series of relative frequencies. This can be readily done bysubstituting the reference values of electrical inductance andcapacitance that I have previously assigned to the analogue electricalcircuit elements in FIGS. 4C and 5B in the formulas governing reactancesin series and reactances in parallel. RL in FIG. 5B is set equal tozero. The formula for series inductive and capacitive reactance (Zs) isas follows:

where: w 2 1r frequency 6.28 frequency For simplification andconvenience, an arbitrary value of 0.159 will be assigned to F resultingin a value of 1.0 for m at this frequency. It is obvious from theformula that where the values of L and C are both equal to 1.0 as inFIG. 4C, the series reactance is equal to zero, thereby producing seriesresonance at F The 2 1r factor being a constant and 1 being equal to 1.0at F the other relative frequencies can be represented by varying thevalue of m. For example, one-half to would represent one-half F and 201would represent twice F The resulting values of series reactance for thedifferent frequencies can thus be calculated for L10 and C10 in FIG. 4C,and for L2and C2 in FIG. 5B.

The values of reactance produced by the paralleling of Cl with L2 C2 canthen be calculated by the use of the general formula for parallelresistance or parallel reactance (Zp), which is:

In this case:

Z, the reactance of Cl 2, the reactance of L2 C2 Having determined thevalue of Zp for the different frequencies, the. values of reactancepresented at the input terminal of the band-pass filter circuit in FIG.58 can be calculated by adding the reactance of L1 to the reactance Zp."

Using this method, I have made up the following chart of reactances vs.frequency as represented by various values of a:

As can be seen from the foregoing chart, the reactances produced by thecircuit of FIG. 4C and those produced by the circuit of FIG. 5B areessentially identical in the frequency region .of 0.25 F up through FAbove F a rising characteristic is evidentfor the circuit of FIG. 5B,which is due to the proximity of the upper cut-off frequency.

As this frequency represents a parallel resonance condition, thereactance is increasingly pushed up as it is approached. Under actualoperating conditions, this phenomenon has little, if any, practicaleffect as will be evidenced by curves made from measurement of theacoustic system operation. Also, there is a series resonance at 2.62 FAlthough this resonance generally has no appreciable effect on theoverall reflected impedance curve, it apparently is associated with acharacteristic hump in radiated sound output in this frequency region.Under some conditions vof adjustment, this resonance mayresult in anadditional reflected electrical impedance peak.

In this particular application, however, the purpose of the filter shownin solid lines in FIG. 5A is to absorb the energy in its pass-bandrather than to transmit it on. A terminating resistance or load" is,therefore, required to absorb the energy. While the low-loss requirementholds true for Ia-2a and Ca-2a, certain losses in conjunction with Ia-2band Ca-2b may function in the correct manner of load resistance.Specifically, flow resistance in conjunction with la-2b and loss fromsound-absorbing material within Ca-2b can be used for the requiredresistive termination. Any loss in Ia-Za will dissipate a proportionateamount of the reflected energy required to produce the extended bassrange. Such loss should, therefore, be minimized.

It is difficult to define just how much loss can be tolerated in respectto the coupling aperture between the first and second1cavities, andin'respect to the first sub-cavity, as the effect is relative and,therefore, dependent on the system performance requirements. Theeffective loss due to the coupling aperture is doubled as the reflectedenergy must make the transit twice. l-lowever, such loss as wasassociated with the 16 one-halfinch holes, used as the aperture means inthe system of FIG. 3A, would not seriously derogate system performance.The phase of port radiation relative to that of the speaker front-wavein the frequency region below F is the best criterion in this respect.Failure of port radiation to support the speaker front-wave is a primeindicator of inadequate efficiency.

I have found that the use of flow-resistance in conjunction with'Ia-2bis analogous to the terminating resistance RL in the electrical filtercircuit shown in FIG. 5B. In the electrical case, the correct value ofterminating resistance is equal to V L/C. There is a' correspondinglycorrect criterion for the acoustic terminating resistance. I havesuccessively employed the same mechanism of flow-resistance that I havedescribed previously herein. I increased the number of holes so as toprovide the required reduction of total aperture inertance. A diagram ofthe acoustic configuration is shown in FIG. 6A. The effective absorptionof energy in the response valley region is evident from the resultingreflected electrical impedance characteristic which is illustrated bycurve in FIG. 68. It can be seen that the effect on the lower frequencyregion is relatively minor. The resulting radiated sound pressurecharacteristicis illustrated by the solid curve in FIG. 6C. The dottedcurve is shown with it for reference, as it is a duplication of thesolid curve in FIG. 3D, which is the radiated sound pressurecharacteristic of the coupling aperture damped two-cavity system modeledafter Leon. The same 6 db/octave low-frequency amplifier compensationwas employed in both cases. As shown by the solid curve of FIG. 6C, theresponse valley of FIG. 4B is eliminated by the modifications of thesecond cavity, and the lower frequency response is essentiallyunaltered.

The use of sound-absorbing material within the second subcavity as shownin FIG. 6D produces results that are substantially the same as theincorporation of flow resistance in Ia-2b (FIG. 6A). However, this typeof damping is distributed and may have an effect on the tuning of thesub-cavities. The effect I have encountered is one of decreasing theeffective capacitance of the first sub-cavity, while increasing theefiective capacitance of the second. While this effect will vary withdifferent types of material, I have found that it can generally becountered by making the first subcavity 113 10 percent larger in volumethan the second 116, the sum of the two volumes being the same asbefore, and the first coupling aperture 111 being the same. The secondcouplingaperture 114 can usually also be the same, but some alterationmay be required to optimize the tuning frequency. I prefer this type oftermination because I have found it easier to work with and it canprovide additional low-frequency selectivity.

The approach that I have used is to fill the entire second sub-cavity116 with sound-absorbing material. I have found that shredded cottonbatten and similar materials work well. The inter sub-cavity couplingaperture must be so shaped as to retain the material. For example, itmay be composed of one or more slots, separate or crossed, or it mayconsist of a group of holes. Also, screening may be used to retain thematerial. The material packing density is important. The optimum packingdensity may be determined empirically, using the reflected impedancecharacteristic as a guide. A diagram of this type of enclosureconfiguration is illustrated in FIG. 6D.

The radiated sound pressure curves that I have shown in FIGS. 3D, 4B and6C are all based on the use of the same given size of speaker, enclosureinternal volume and second cavity resonance frequency, as described.Where the second cavity is modified into a band-pass filter, the lowercut-off frequency is the same as the resonance frequency of theunmodified second cavity. This resonance frequency, which I havereferred to as F is generally the same as the speaker cone resonancefrequency F,.. This relationship, however, is not at all critical, asthe basic phase and amplitude relationships that extend the bass rangeare primarily a function of the enclosure configuration and adjustment.That is, the movement of the speaker cone at any given instance is theinitiating phenomenon for the action and reaction of energy within theenclosure. Therefore, such action and reaction as occurs isautomatically phase referenced to the speaker cone movement.

The important relationships are those between P the effective pistonarea of the speaker cone and the enclosure internal volume. I have foundit necessary to hold these relationships within reasonable limits if asmooth transition between the response in the base frequency region andthe response to the upper frequencies is to be realized. Theserelationships have been optimum in the examples that I have so fardescribed. If the internal volume of the enclosure is too small relativeto the cone area and F the acoustic back-wave impedance will interferewith the ability of the cone to respond at the lower frequencies,resulting in low relative bass efficiency and uneven response in thetransition region. If the enclosure volume is larger than optimum, thebass efficiency will be too high and the bass response level will appearas a plateau lifted above the level of the upper frequencies. Theseeffects tend to be independent of the hinge point used for the amplifierfrequency response compensation, and find their source in the ratio ofacoustic back-wave impedance to the front-wave radiation impedance. 1have found that the back-wave impedance is inversely proportionate to F,where the overall effective enclosure volume is held constant. a

In accordance with this invention, I have discovered an optimum relationamong enclosure sizes, speaker sizes, and frequency ranges, and I havedeveloped a generalized formula for optimizing these relationships. Bythe use of this formula, speaker enclosures of this type can be scaledin respect to internal volume for speakers of different cone areas andfor different frequency ranges. The formula is as follows:

V total efiective volume of the internal air space in the completeenclosure in cubic feet A effective piston area of the speaker cone insquare inches F frequency at which the reactance of said couplingaperture means is equal to and of opposite sign to that of said secondcavity The above value of V may vary from 8096 to I -4()%, while stillretaining satisfactory and acceptable results within this invention.

My use of the word aperture is intended to include any means foraccomplishing an acoustical inertance function equivalent to thatdisclosed above. For example, the acoustical inertance function may beperformed by more than one opening and the opening or openings mayinclude ducting or the function might be performed by one or morediaphragms which perform the coupling and inertance function. Also, asin the case of the inter sub-cavity coupling aperture, the acousticalinertance function may in some instances be physically combined with anacoustical resistance function and cavity division function through theemployment of .a porous or breathing type of dividing wall material. Insuch a case, the function is nonetheless accomplished, and the reactivecomponent of the impedance thus produced should be considered in the Thesame type of considerations apply to my use of the words cavity andsub-cavity." For example, a block of porous material having suchphysical properties as to perform in the manner of a lossy resonantdielectric could function as the second sub-cavity in the second cavitymodification. In such a case the inertance, capacitance and resistancewould be inseparably distributed throughout the block. A portion, or oneor more, of the block surfaces could function both as the means ofdivision of the second cavity into sub-cavities and as the inertancecoupling the two subcavities together. Although some of the acousticelements may in some instances be physically inseparable, essentiallythe same basic relationships between the effective reactances must existand should be taken into account in the determination of F Thepermissible amount of down-side deviation in enclosure volume from thatdictated by the formula is largely a matter of how much performancederogation the designer can tolerate. For example, the solid curve inFIG. 7 shows the typical effect of selecting a volume of only one-halfthat of optimum per the formula, the dotted curve being thecharacteristic with optimum enclosure volume. In most instances thismuch derogation would not be tolerable. However, where the system is tobe operated at the intersection of two perpendicular planes, theradiation resistance is improved at the lower frequencies and theproblem is partially alleviated. Therefore, a tolerance of -40 percentis representative of the maximum that could typically be tolerated underthis condition.

Under the theoretical condition where the driving impedance of thespeaker is matched to the acoustic impedance of the enclosure at optimumvolume, a decrease of 40 percent in bass radiated sound power or -2.2db. Likewise, under the same theoretical condition, an increase inenclosure volume of percent over optimum will result in an increase ofradiated bass sound power of 66 percent or +2.2 db. Under practicalconditions where a matched driving impedance is not realized, the lossor gain from deviation from optimum enclosure volume may besubstantially greater as the solid curve in FIG. 7 indicates. Althoughit might appear that a deviation in either direction from optimum wouldresult in a drop in sound output, the radiated sound output power isproportional to the square of volume current produced by the speakercone movement rather than the amount of sound power delivered to theinterior of the enclosure. Hence, an increase in enclosure volumeresults in a lower acoustic impedance, thus increasing the volumecurrent and, hence, the radiated sound power output. Deviation on theup-side is, therefore, not as critical as deviation on the down-side, asit increases bass efficiency.

Whilethe volume tolerance of 40 percent and +80 percent may appearbroad, when related to the mean linear dimensional variation of theactual physical structure, they are quite restrictive. The mean lineardimension is substantially proportional to the cube root of volume, andin the case of a cube, it is exactly so. Referencing then to the cuberoot of volume, the tolerancesmay be stated as J1 l8 percent to +215percent.

The basic two-cavity systems described have been shown as havingcavities Ca-l and Ca-2 of equal volume. While this relationship givesgood performance, fairly good performance may also be obtained withunequal volumes. It is important, however, to have the overall internalvolume in correspondence with the relationships I have given in myformula for enclosure volume.

Using the same loudspeaker and internal volume as before, I have set upand evaluated samples of differing cavity volumes, for example, dividingthe enclosure so that the second cavity volume was twice that of thefirst. The second cavity was tuned to the correct frequency for thespeaker cone area and enclosure internal volume, and then modified intoa band-pass filter as described herein. Flow-resistance damping of thesecond sub-cavity coupling aperture was employed as an acousticresistance termination for the band-pass filter sub-system. A diagram ofthe modified configuration is shown in FIG. 8A. The reflected electricalimpedance characteristic before modifying the second cavity with thepartition 131 is shown by the solid curve in FIG. 8B. The dotted curvein FIG. 8B shows the reflected impedance with the second cavityconverted into the band-pass filter sub-system, as shown in FIG. 8A. Theradiated sound pressure response charac teristic of FIG. 8A is shown bythe dash curve in FIG. 8B;

As can be seen from the curves in FIG. 8B, the response of the system isstill fairly good. The reflected impedance curves point up one of thecharacteristics of this type of system, which is, as the ratio of secondcavity volume to first-cavity volume increases, the spread between theimpedance peaks increases and the middle impedance peak become moredominant. As can also be seen, the variation in impedance peak spread isnot sufficient to significantly interfere with the application of mysecond-cavity modification technique. My investigations indicate thatuseful performance can be obtained over a range of 0.4 to 1.8 in theratio of firstcavity volume to second-cavity volume.

I have found that my second-cavity modification technique is alsoapplicable to the type of basic twocavity system wherein the externalport aperture is located in the second cavity. Also, my formula forscaling enclosure volume is applicable. The basic acoustic configurationis illustrated by the diagram in FIG. 9A. The relationships of theacoustic element values are such that the capacitance of the firstcavity will resonate with the inertance of the port aperture at thefrequency F and the capacitance of the second cavity will resonate withthe inertance of the coupling aperture, likewise at F,. The reflectedelectrical impedance characteristic is shown by the dotted curve in FIG.9B, and the radiated sound pressure characteristic is shown by dottedcurve in FIG. 9C.

The modification technique is the same as before, with the exceptionthat the port aperture is located in the first sub-cavity.

A diagram of this modified system is shown in FIG. 9D.

Although the functioning of this type of system is different from thatof FIGS. 4A and 5A, the basic relationships of the reactive acousticelements are again such that, where the acoustic tennination resistanceis equal to zero in the modified system of FIG. 9D, its acousticfunctioning is essentially the same as that of the unmodified system ofFIG. 9A. In applying my formula for enclosure volume to this type ofsystem, P is determined by the conditions that exist when the portaperture is sealed off.

The reflected impedance characteristic with the modifications, includingthe acoustic terminating resistance, is shown by the solid curve in FIG.9B. These curves were based on data taken with the use of the same Altecloudspeaker and the same 1.2 cubic feet internal enclosure volume, andthe same low-frequency amplifier compensation was employed. It can beseen that the bass range of this type of system is inferior to thatwhere the port is in the first cavity, although the response isotherwise very uniform.

I have also found an additional technique for improving the bassresponse range and acoustic cone loading where the port aperture is inthe first cavity. I have found that the relative phase relationship ofthe motion of the speaker cone and the motion of air at the portaperture is such that increased-cone loading or effective radiationresistance can be achieved by directing this air motion toward the areaimmediately in front of the speaker cone. As shown in FIG. 10A, the portaperture can be split into two slots 141 and 142, one on either side ofthe speaker 143, and louvres or deflectors 146 and 147, respectively,used to direct the air motion equally and oppositely toward the speaker,thus maximizing the advantage. Also, the improvement can generally beeffected by tuning the port aperture (or apertures) so that itsresonance with the first cavity is at a somewhat lower frequency thanF,.

The advantages realized from the use of port aperture deflectioncomprise an improvement on the order of 1.5 db in both power handlingability and sound power output in the low end of the bass range.

Orthogonal views of a model employing the port aperture deflection andinertance adjustment as

1. A loudspeaker system comprising: first cavity means constituted by anenclosing wall means and confined air space and functionally operable asan acoustic capacitance; loudspeaker means mounted to and forming aportion of said wall means of said first cavity means; second cavitymeans constituted by an enclosing wall means and confined air space andfunctionally operable as an acoustic capacitance; coupling aperturemeans functionally operable as an acoustic inertance linking theacoustic capacitance of said first cavity to the acoustic capacitance ofsaid second cavity; the inertance of said coupling aperture meansproducing a value of acoustic reactance that is equal to and of oppositesign to the acoustic reactance produced by the effective acousticcapacitance of said second cavity means at some specific frequency, F;port aperture means in a side wall means functionally operable as anacoustic inertance linking the acoustic capacitance of one of saidcavities to the radiation impedance of the exterior system atmosphere;said loudspeaker system producing a radiated sound pressure vs.frequency curve characterized by a band of response below F, whereinradiation from said port aperture means supports the front-waveradiation from said loudspeaker; and wherein the sum of the effectiveinternal air space of said first cavity means plus the effectiveinternal air space of said second cavity means, the effective cone areaof said loudspeaker means, and F are related substantially in accordancewith the following formula: V 2.9 A/F + 80% - 40% Where: V totaleffective internal air space of cavity means, in cubic feet A effectivepiston area of loudspeaker cone, in square inches F frequency at whichthe reactance of said coupling aperture means is equal to and ofopposite sign to that of said second cavity means.
 2. System as in claim1, wherein the ratio of said internal air space of said first cavitymeans to that of said second cavity means falls within the range of 0.4to 1.7.
 3. System as in claim 1, wherein said coupling aperture means isan acoustic inertance of relatively good efficiency substantially freeof acoustic resistance.
 4. System as in claim 1, wherein said portaperture means is in the enclosing wall means of said first cavitymeans.
 5. System as in claim 1, wherein said port aperture means is inthe enclosing wall means of said second cavity means.
 6. System as inclaim 2, wherein said coupling aperture means is an element of acousticinertance of relatively good efficiency substantially free of acousticresistance.
 7. System as in claim 1, wherein said port aperture means islocated in said first cavity means; and including also deflection meanscooperatively operable with said port aperture means whereby soundenergy emanating from said port aperture means is directed toward thearea immediately in front of said loudspeaker means.
 8. A loudspeakersystem comprising: first cavity means constituted by an enclosing wallmeans and confined air space and functionally operable as an element ofacoustic capacitance; loudspeaker means mounted to and forming a portionof said wall means of said first caviTy means; second cavity meansconstituted by an enclosing wall means and confined air space adjoinedto said first cavity means and functionally operable as an element ofacoustic capacitance; coupling aperture means functionally operable asan acoustic inertance linking the acoustic capacitance of said firstcavity to the acoustic capacitance of said second cavity; the inertanceof said coupling aperture means producing a value of acoustic reactancethat is equal to and of opposite sign to the acoustic reactance producedby the acoustic capacitance of said second cavity means at a specificfrequency F; port aperture means functionally operable as an element ofacoustic inertance linking the acoustic capacitance of one of saidcavities to the radiation impedance of the exterior system atmosphere;said loudspeaker system, when unmodified, producing a radiated soundpressure vs. frequency curve characterized by a response band below Fwherein port aperture radiation is additive to said loudspeakerfront-wave radiation, followed by a valley in response in the regionabove F; second cavity modification means for modifying said secondcavity means and said coupling aperture means to cooperatively functionas band-pass filter means and comprising; division means separating saidsecond cavity means into first sub-cavity means and second sub-cavitymeans, said first sub-cavity means and said second sub-cavity means eachfunctionally operable as elements of acoustic capacitance; the sum ofthe acoustic capacitance of said first sub-cavity means being equal tothe unmodified said second cavity means; said division meansincorporating sub-cavity coupling aperture means functionally operableas an element of acoustic inertance and linking the acoustic capacitanceof said first sub-cavity means to the acoustic capacitance of saidsecond sub-cavity means; the acoustic reactance produced by theinertance of said sub-cavity coupling aperture means being equal to andof opposite sign to the acoustic reactance produced by the acousticcapacitance of said second sub-cavity means at a frequency in the regionof said response valley; the acoustic inertance of said sub-cavitycoupling aperture means and the acoustic capacitance of said secondsub-cavity means cooperatively functioning as termination arm in saidband-pass filter means; the acoustic inertance of said coupling aperturemeans and the acoustic capacitance of said first sub-cavity couplingaperture means cooperatively functioning as transmission arm means insaid band-pass filter means; the acoustic reactance produced by theacoustic inertance of said coupling aperture means being equal to and ofopposite sign to the acoustic reactance produced by the acousticcapacitance of said first sub-cavity means at a frequency in the regionof said response valley; wherein, at said frequency F, reactanceproduced by the inertance of said sub-cavity coupling aperture means andthe capacitance of said second sub-cavity means as combined with thereactance produced by the capacitance of said first sub-cavity meansresults in a value of acoustic reactance that is substantially equal toand of opposite sign to the value of reactance produced by the inertanceof said coupling aperture means as modified; said termination arm meansincorporating substantial damping means; whereby said band-pass filtermeans selectively absorbs and dissipates sound energy in the frequencyregion of said response valley; and whereby said band-pass filter meansfunctions essentially in the same manner as the unmodified said secondcavity means and the unmodified said coupling aperture means in thefrequency region below said frequency F, said modification means havingsubstantially no effect on said response band below F, while raisingsubstantially said valley.
 9. System as in claim 8, wherein the ratio ofthe acoustic capacitance of said first caviTy means to the acousticcapacitance of said second cavity means falls within the range of 0.4 to1.7.
 10. System as in claim 8, wherein said coupling aperture means isan acoustic inertance of relatively good efficiency substantially freeof acoustic resistance.
 11. System as in claim 8, wherein the sum ofeffective air space of said first cavity means plus the effective airspace of said second cavity means, the effective cone area of saidloudspeaker means, and the frequency F are related substantially inaccordance with the following formula: V 2.9 A/F + 80% - 40% Where: Vtotal effective internal air space of cavity means in cubic feet Aeffective piston area of loudspeaker cone in square inches F frequencyat which the reactance of said coupling aperture means is equal to andof opposite sign to that of said second cavity means.
 12. System as inclaim 8, wherein said port aperture means is located in said enclosingwall means of said first cavity means.
 13. System as in claim 8, whereinsaid port aperture means is located in said enclosing wall means of saidfirst sub-cavity means; and wherein said port aperture means isfunctionally operable as an element of acoustic inertance linking theacoustic capacitance of said first sub-cavity means to the radiationimpedance of the external system atmosphere.
 14. System as in claim 8,wherein said port aperture means is located in said first cavity means;and including also deflection means cooperatively operable with saidport aperture means, whereby sound energy emanating from said portaperture means is directed toward the area immediately in front of saidloudspeaker means.
 15. A loudspeaker system comprising: first cavitymeans constituted by an enclosing wall means and confined air space andfunctionally operable as an element of acoustic capacitance; loudspeakermeans mounted to and forming a portion of said wall means of said firstcavity means; second cavity means constituted by an enclosing wall meansand confined air space adjoined to said first cavity means andfunctionally operable as an element of acoustic capacitance; couplingaperture means functionally operable as an acoustic inertance linkingthe acoustic capacitance of said first cavity to the acousticcapacitance of said second cavity; the inertance of said couplingaperture means producing a value of acoustic reactance that is equal toand of opposite sign to the acoustic reactance produced by the effectiveacoustic capacitance of said second cavity means at a specific frequencyF; port aperture means functionally operable as an element of acousticinertance linking the acoustic capacitance of one of said cavity meansto the radiation impedance of the exterior system atmosphere; saidloudspeaker system, when unmodified, producing a radiated sound pressurevs. frequency curve characterized by a response band below F, whereinport aperture radiation is additive to said loudspeaker front waveradiation, followed by a valley in response in the region above F;second cavity modification means for modifying said second cavity meansand said coupling aperture means so that their cooperative function isessentially that of a single cavity means and single aperture means inthe frequency region below F, while also functioning as a frequencyselective sound energy absorption means in the frequency region of saidresponse valley, said modification means having substantially no effecton said response band below F, while raising substantially said valley.16. System as in claim 15, wherein said second cavity means isfunctionally operable as a band-pass filter means, and includes:division means separating said second cavity means into first sub-cavitymeans and second sub-cavity means, said first sub-cavity means and saidsecond sub-cavity Means each functionally operable as elements ofacoustic capacitance.
 17. System as in claim 15, wherein the ratio ofthe acoustic capacitance of said first cavity means to the acousticcapacitance of said second cavity means falls within the range of 0.4 to1.7.
 18. System as in claim 15, wherein said coupling aperture meansfunctions as an acoustic inertance of relatively good efficiency. 19.System as in claim 15, wherein the sum of the effective air space ofsaid first cavity means plus the effective air space of said secondcavity means, the effective cone area of said loudspeaker means, and thefrequency Fr-C2 are related substantially in accordance with thefollowing formula: V 2.9 A/F + 80% - 40% Where: V total effectiveinternal air space of cavity means in cubic feet A effective piston areaof loudspeaker cone in square inches F frequency at which the reactanceof said coupling aperture means is equal to and of opposite sign to thatof said second cavity means.
 20. System as in claim 15, wherein saidport aperture means is located in said enclosing wall means of saidfirst cavity means.
 21. System as in claim 15, wherein said portaperture means is located in said enclosing wall means of said secondcavity means; and wherein said port aperture means is functionallyoperable as an element of acoustic inertance linking the acousticcapacitance of said first sub-cavity means to the radiation impedance ofthe external system atmosphere.
 22. System as in claim 15, and theincorporation of deflection means cooperatively operable with said portaperture means, whereby sound energy emanating from said port aperturemeans is directed toward the area immediately in front of saidloudspeaker means.